Turbulent Spatio-Temporal Dynamics in Reacting-Diffusing Systems: Results for a Soluble Model

A class of soluble three "species" reaction-diffusion type systems is presented Exact solutions are obtained which show turbulent spatio-temporal evolution All homogeneous evolution tends asymptotically toward an attractor which is shown to be a two layered two dimensional manifold in the three dimensional species space. Sustained aperiodic spatio-temporal solutions are also found.